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BBGKY Hierarchy
In statistical physics, the BBGKY hierarchy (Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy, sometimes called Bogoliubov hierarchy) is a set of equations describing the dynamics of a system of a large number of interacting particles. The equation for an ''s''-particle distribution function (probability density function) in the BBGKY hierarchy includes the (''s'' + 1)-particle distribution function, thus forming a coupled chain of equations. This formal theoretic result is named after Nikolay Bogolyubov, Max Born, Herbert S. Green, John Gamble Kirkwood, and Jacques Yvon. Formulation The evolution of an ''N''-particle system in absence of quantum fluctuations is given by the Liouville equation for the probability density function f_N = f_N(\mathbf_1 \dots \mathbf_N, \mathbf_1 \dots \mathbf_N, t) in 6''N''-dimensional phase space (3 space and 3 momentum coordinates per particle) : \frac + \sum_^N \frac \frac + \sum_^N \mathbf_i \frac = 0, where \mathbf_i, \mathbf_ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harold Grad
Harold Grad (January 23, 1923 in New York City – November 17, 1986) was an American applied mathematician. His work specialized in the application of statistical mechanics to plasma physics and magnetohydrodynamics. Work In statistical mechanics he had developed in his thesis new methods for the solution of the Boltzmann equation. He derived the Boltzmann equation from Liouville equation using BBGKY hierarchy under certain limits, known as Boltzmann–Grad limit. Harold Grad was the founder of the Magneto-fluid Dynamics Division of the Courant Institute and served as its head until shortly before his death From 1964 to 1967 and 1974 to 1977 he was a member of the Advisory Committee for Fusion Energy at Oak Ridge National Laboratory. Grad was a critic and supporter of many early fusion schemes including picket fences, magnetic mirrors and Biconic cusps. Recognition In 1970, Grad became a member of the National Academy of Sciences. He was an invited speaker at the Internati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Physics
Statistical physics is a branch of physics that evolved from a foundation of statistical mechanics, which uses methods of probability theory and statistics, and particularly the Mathematics, mathematical tools for dealing with large populations and approximations, in solving physical problems. It can describe a wide variety of fields with an inherently stochastic nature. Its applications include many problems in the fields of physics, biology, chemistry, and neuroscience. Its main purpose is to clarify the properties of matter in aggregate, in terms of physical laws governing atomic motion. Statistical mechanics develop the Phenomenology (particle physics), phenomenological results of thermodynamics from a probabilistic examination of the underlying microscopic systems. Historically, one of the first topics in physics where statistical methods were applied was the field of classical mechanics, which is concerned with the motion of particles or objects when subjected to a force. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Mechanics
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic behavior of nature from the behavior of such ensembles. Statistical mechanics arose out of the development of classical thermodynamics, a field for which it was successful in explaining macroscopic physical properties—such as temperature, pressure, and heat capacity—in terms of microscopic parameters that fluctuate about average values and are characterized by probability distributions. This established the fields of statistical thermodynamics and statistical physics. The founding of the field of statistical mechanics is generally credited to three physicists: *Ludwig Boltzmann, who developed the fundamental interpretation of entropy in terms of a collection of microstates *James Clerk Maxwell, who developed models of probability distr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cluster-expansion Approach
The cluster-expansion approach is a technique in quantum mechanics that systematically truncates the BBGKY hierarchy problem that arises when quantum dynamics of interacting systems is solved. This method is well suited for producing a closed set of numerically computable equations that can be applied to analyze a great variety of many-body and/or quantum-optical problems. For example, it is widely applied in semiconductor quantum opticsKira, M.; Koch, S. W. (2011). ''Semiconductor Quantum Optics''. Cambridge University Press. and it can be applied to generalize the semiconductor Bloch equations and semiconductor luminescence equations. Background Quantum theory essentially replaces classically accurate values by a probabilistic distribution that can be formulated using, e.g., a wavefunction, a density matrix, or a phase-space distribution. Conceptually, there is always, at least formally, probability distribution behind each observable that is measured. Already in 1889, a lo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vlasov Equation
The Vlasov equation is a differential equation describing time evolution of the Distribution function (physics), distribution function of plasma (physics), plasma consisting of charged particles with long-range interaction, e.g. Coulomb's law, Coulomb. The equation was first suggested for description of plasma by Anatoly Vlasov in 1938 and later discussed by him in detail in a monograph. Difficulties of the standard kinetic approach First, Vlasov argues that the standard kinetic theory of gases, kinetic approach based on the Boltzmann equation has difficulties when applied to a description of the plasma with long-range Coulomb's law, Coulomb interaction. He mentions the following problems arising when applying the kinetic theory based on pair collisions to plasma dynamics: # Theory of pair collisions disagrees with the discovery by John Strutt, 3rd Baron Rayleigh, Rayleigh, Irving Langmuir and Lewi Tonks of natural vibrations in electron plasma. # Theory of pair collisions is formal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fokker–Planck Equation
In statistical mechanics, the Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of the velocity of a particle under the influence of drag forces and random forces, as in Brownian motion. The equation can be generalized to other observables as well. It is named after Adriaan Fokker and Max Planck, who described it in 1914 and 1917. It is also known as the Kolmogorov forward equation, after Andrey Kolmogorov, who independently discovered it in 1931. When applied to particle position distributions, it is better known as the Smoluchowski equation (after Marian Smoluchowski), and in this context it is equivalent to the convection–diffusion equation. The case with zero diffusion is the continuity equation. The Fokker–Planck equation is obtained from the master equation through Kramers–Moyal expansion. The first consistent microscopic derivation of the Fokker–Planck equation in the single schem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Chemical Physics
''The Journal of Chemical Physics'' is a scientific journal published by the American Institute of Physics that carries research papers on chemical physics."About the Journal" from the ''Journal of Chemical Physics'' website. Two volumes, each of 24 issues, are published annually. It was established in 1933 when '''' editors refused to publish theoretical works. The editors have been: *2019-present: Tim Lian *2008–2018: *2007–2008: [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacques Yvon
Ancient and noble French family names, Jacques, Jacq, or James are believed to originate from the Middle Ages in the historic northwest Brittany region in France, and have since spread around the world over the centuries. To date, there are over one hundred identified noble families related to the surname by the Nobility & Gentry of Great Britain & Ireland. Origins The origin of this surname ultimately originates from the Latin, Jacobus which belongs to an unknown progenitor. Jacobus comes from the Hebrew name, Yaakov, which translates as "one who follows" or "to follow after". Ancient history A French knight returning from the Crusades in the Holy Lands probably adopted the surname from "Saint Jacques" (or "James the Greater"). James the Greater was one of Jesus' Twelve Apostles, and is believed to be the first martyred apostle. Being endowed with this surname was an honor at the time and it is likely that the Church allowed it because of acts during the Crusades. Indeed, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kirill Gurov
Kirill Gurov (6 March 1918 – 29 September 1994) was a Soviet Russian theoretical physicist working in the field of physical kinetics. Gurov was born in Moscow, Russia, in the family of a military officer. In 1936, he was accepted without examinations to the Faculty of Physics and Mathematics in Moscow State University (MSU) and graduated from MSU in 1941, earning a Diploma with Honour. In 1944, he started to work in MSU as a PhD student, under the supervision of Nikolay Bogolyubov, on problems of kinetic theory of quantum systems. From 1954, and for the rest of his life, Kirill Gurov worked at the A. A. Baikov Institute of Metallurgy and Material ScienceIMMS. Research Kirill Gurov and Nikolay Bogolyubov obtained kinetic equations for quantum systems by developing the method of quantum BBGKY hierarchy. At the IMMS, Kirill Gurov worked on analysis of the diffusion processes and the corresponding phase transitions in alloy An alloy is a mixture of chemical elements of w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
JETP
The ''Journal of Experimental and Theoretical Physics'' (''JETP'') [russian: Журнал Экспериментальной и Теоретической Физики, italic=yes (''ЖЭТФ''), or ''Zhurnal Éksperimental'noĭ i Teoreticheskoĭ Fiziki'' (''ZhÉTF'')] is a peer-reviewed Russian bilingual scientific journal covering all areas of experimental and theoretical physics. For example, coverage includes solid state physics, elementary particles, and cosmology. The journal is published simultaneously in both Russian and English languages. The editor-in-chief An editor-in-chief (EIC), also known as lead editor or chief editor, is a publication's editorial leader who has final responsibility for its operations and policies. The highest-ranking editor of a publication may also be titled editor, managing ... is Alexander F. Andreev. In addition, this journal is a continuation of ''Soviet physics, JETP'' (1931–1992), which began English translation in 1955. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nikolay Bogoliubov
Nikolay Nikolayevich Bogolyubov (russian: Никола́й Никола́евич Боголю́бов; 21 August 1909 – 13 February 1992), also transliterated as Bogoliubov and Bogolubov, was a Soviet and Russian mathematician and theoretical physicist known for a significant contribution to quantum field theory, classical and quantum statistical mechanics, and the theory of dynamical systems; he was the recipient of the 1992 Dirac Medal. Biography Early life (1909–1921) Nikolay Bogolyubov was born on 21 August 1909 in Nizhny Novgorod, Russian Empire to Russian Orthodox Church priest and seminary teacher of theology, psychology and philosophy Nikolay Mikhaylovich Bogolyubov, and Olga Nikolayevna Bogolyubova, a teacher of music. The Bogolyubovs relocated to the village of Velikaya Krucha in the Poltava Governorate (now in Poltava Oblast, Ukraine) in 1919, where the young Nikolay Bogolyubov began to study physics and mathematics. The family soon moved to Kiev in 1921, wher ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
